Making private sales safer

I’ve bought and sold a small number of guns in private sales over the years, mostly with friends I’ve known for decades and others I know are non-prohibited (e.g. I watched them pass a NICS check a week or two before) so the risk of my inadvertently selling to a prohibited person was quite small. Still, I was thinking about ways to make private sales safer for both buyer and seller.
It seems to me that the most logical thing would be to perform a NICS (or equivalent) check when issuing drivers licenses or state IDs. People who pass the check get a green checkmark or something on the back of their license, while those who fail get a red “X” or some other mark. It doesn’t need to be huge or obvious (think “Organ Donor”-mark sized), and it doesn’t even need to suggest guns (so squeamish people don’t get annoyed or even know what the mark is for).
Since everyone, gun owner or not, gets the marks on their drivers license or state ID, there’s no privacy risk that could be used to identify who is a gun owner or who isn’t. The marks merely indicate if someone is or is not prohibited from owning guns.
If someone’s circumstances change so that they’re now prohibited from possessing guns,?their license is replaced with one with the “prohibited” mark. Since such a change in circumstance almost always involves the authorities (e.g. being arrested by the cops, tried in court, etc.) enforcement should be reasonably easy. Costs would be negligible, since similar checks to determine one’s eligibility to drive are already carried out by the DMV at the time of issuance.
Those participating in private sales can easily check for the “approved” mark and have confidence that they’re dealing with a non-prohibited person.
Criminals would, as they do already, engage in illegal sales without compunction and wouldn’t care about marks on licenses. That’s not what this proposal is intended to stop: I’m interested in making it easier for people to buy or sell guns privately without inadvertently selling to or buying from a prohibited person.
In short, like Illinois’ FOID cards, only without needing to specifically apply for a separate license that uniquely identifies them as a firearms owner.
Of course, since this?proposal has no possibility for backdoor registration, I’m pretty sure the anti-gun folks aren’t remotely interested.

Does it?
My idea was simply to provide additional information to people engaged in private sales so they don’t inadvertently transfer a gun to a prohibited person, all while not needing to ask permission from the government.
I know such inadvertent sales are rare, but the current system of either using an FFL to mediate a private sale (which has privacy implications) or trusting the other person to be non-prohibited (which can be problematic if the other person is not well-known to you) doesn’t sit well with me. I’d like to fix the latter situation so people can be reasonably assured that the person they’re selling to/buying from is not prohibited.